When Trees Collide: An Approximation Algorithm for the Generalized Steiner Problem on Networks
 Citation data:

SIAM Journal on Computing, ISSN: 00975397, Vol: 24, Issue: 3, Page: 440456
 Publication Year:
 1995
 Repository URL:
 http://repository.cmu.edu/tepper/357
 DOI:
 10.1137/s0097539792236237
 Author(s):
 Publisher(s):
 Tags:
 Computer Science; Mathematics; approximation algorithm; network design; Steiner tree problem; Economic Policy; Economics; Industrial Organization
article description
We give the first approximation algorithm for the generalized network Steiner problem, a problem in network design. An instance consists of a network with linkcosts and, for each pair {i, j} of nodes, an edgeconnectivity requirement r. The goal is to find a minimumcost network using the available links and satisfying the requirements. Our algorithm outputs a solution whose cost is within 2[log(r + 1)] of optimal, where r is the highest requirement value. In the course of proving the performance guarantee, we prove a combinatorial minmax approximate equality relating minimumcost networks to maximum packings of certain kinds of cuts. As a consequence of the proof of this theorem, we obtain an approximation algorithm for optimally packing these cuts; we show that this algorithm has application to estimating the reliability of a probabilistic network.